The Gravitational Universe

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(1)The Gravitational Universe A science theme addressed by the eLISA mission observing the entire Universe. Prof. Dr. Karsten Danzmann Albert Einstein Institute Hannover MPI for Gravitational Physics and Leibniz Universität Hannover Callinstr. 38 30167 Hannover Germany karsten.danzmann@aei.mpg.de Tel.: +49 511 762 2229 Fax: +49 511 762 2784. Detailed information at http://elisascience.org/whitepaper. The last century has seen enormous progress in our understanding of the Universe. We know the life cycles of stars, the structure of galaxies, the remnants of the big bang, and have a general understanding of how the Universe evolved. We have come remarkably far using electromagnetic radiation as our tool for observing the Universe. However, gravity is the engine behind many of the processes in the Universe, and much of its action is dark. Opening a gravitational window on the Universe will let us go further than any alternative. Gravity has its own messenger: Gravitational waves, ripples in the fabric of spacetime. They travel essentially undisturbed and let us peer deep into the formation of the first seed black holes, exploring redshifts as large as z ~ 20, prior to the epoch of cosmic re-ionisation. Exquisite and unprecedented measurements of black hole masses and spins will make it possible to trace the history of black holes across all stages of galaxy evolution, and at the same time constrain any deviation from the Kerr metric of General Relativity. eLISA will be the first ever mission to study the entire Universe with gravitational waves. eLISA is an all-sky monitor and will offer a wide view of a dynamic cosmos using gravitational waves as new and unique messengers to unveil The Gravitational Universe. It provides the closest ever view of the early processes at TeV energies, has guaranteed sources in the form of verification binaries in the Milky Way, and can probe the entire Universe, from its smallest scales around singularities and black holes, all the way to cosmological dimensions..

(2) !"#$%&' Pau Amaro Seoane, Sofiane Aoudia, Gerard Auger, Stanislav Babak, Enrico Barausse, Massimo Bassan, Volker Beckmann, Pierre Binétruy, Johanna Bogenstahl, Camille Bonvin, Daniele Bortoluzzi, Julien Brossard, Iouri Bykov, Chiara Caprini, Antonella Cavalleri, Monica Colpi, Giuseppe Congedo, Karsten Danzmann, Luciano Di Fiore, Marc Diaz Aguilo, Ingo Diepholz, Rita Dolesi, Massimo Dotti, Carlos F. Sopuerta, Luigi Ferraioli, Valerio Ferroni, Noemi Finetti, Ewan Fitzsimons, Jonathan Gair, Domenico Giardini, Ferran Gibert, Catia Grimani, Paul Groot, Hubert Halloin, Gerhard Heinzel, Martin Hewitson, Allan Hornstrup, David Hoyland, Mauro Hueller, Philippe Jetzer, Nikolaos Karnesis, Christian Killow, Andrzej Krolak, Ivan Lloro, Davor Mance, Thomas Marsh, Ignacio Mateos, Lucio Mayer, Joseph Moerschell, Gijs Nelemans, Miquel Nofrarias, Frank Ohme, Michael Perreur-Lloyd, Antoine Petiteau, Eric Plagnol, Edward Porter, Pierre Prat, Jens Reiche, David Robertson, Elena Maria Rossi, Stephan Rosswog, Ashley Ruiter, B.S. Sathyaprakash, Bernard Schutz, Alberto Sesana, Benjamin Sheard, Ruggero Stanga, Tim Sumner, Takamitsu Tanaka, Michael Tröbs, Hai-Bo Tu, Daniele Vetrugno, Stefano Vitale, Marta Volonteri, Gudrun Wanner, Henry Ward, Peter Wass, William Joseph Weber, Peter Zweifel Affiliations can be found in a detailed list of authors at http://elisascience.org/authors. ( )%*#&+,"#%&' Heather Audley, John Baker, Simon Barke, Matthew Benacquista, Peter L. Bender, Emanuele Berti, Nils Christopher Brause, Sasha Buchman, Jordan Camp, Massimo Cerdonio, Giacomo Ciani, John Conklin, Neil Cornish, Glenn de Vine, Dan DeBra, Marc Dewi Freitag, Germán Fernández Barranco, Filippo Galeazzi, Antonio Garcia, Oliver Gerberding, Lluis Gesa, Felipe Guzman Cervantes, Zoltan Haiman, Craig Hogan, Daniel Holz, C.D. Hoyle, Scott Hughes, Vicky Kalogera, Mukremin Kilic, William Klipstein, Evgenia Kochkina, Natalia Korsakova, Shane Larson, Maike Lieser, Tyson Littenberg, Jeffrey Livas, Piero Madau, Peiman Maghami, Christoph Mahrdt, David McClelland, Kirk McKenzie, Sean McWilliams, Stephen Merkowitz, Cole Miller, Shawn Mitryk, Soumya Mohanty, Anneke Monsky, Guido Mueller, Vitali Müller, Daniele Nicolodi, Samaya Nissanke, Kenji Numata, Markus Otto, E. Sterl Phinney, Scott Pollack, Alix Preston, Thomas Prince, Douglas Richstone, Louis Rubbo, Josep Sanjuan, Stephan Schlamminger, Daniel Schütze, Daniel Shaddock, Sweta Shah, Aaron Spector, Robert Spero, Robin Stebbins, Gunnar Stede, Frank Steier, Ke-Xun Sun, Andrew Sutton, David Tanner, Ira Thorpe, Massimo Tinto, Michele Vallisneri, Vinzenz Wand, Yan Wang, Brent Ware, Yinan Yu, Nicolas Yunes Affiliations can be found in a detailed list of contributors at http://elisascience.org/contributors. ( '"--%&#.&' Among the, roughly, 1000 scientific supporters of the Gravitational Universe science theme, are Gerardus ‘t Hooft Utrecht University (Netherlands), Barry Barish Caltech (United States), Claude Cohen-Tannoudji College de France (France), Neil Gehrels NASA Goddard Space Flight Center (United States), Gabriela Gonzalez LIGO Scientific Collaboration Spokesperson, LSU (United States), Douglas Gough Institute of Astronomy, University of Cambridge (United Kingdom), Stephen Hawking University of Cambridge, DAMTP (United Kingdom), Steven Kahn Stanford University/SLAC National Accelerator Laboratory (United States), Mark Kasevich Stanford University, Physics Dept. (United States), Michael Kramer Max-Planck-Institut fuer Radioastronomie (Germany), Abraham Loeb Harvard University (United States), Piero Madau University of California, Santa Cruz (United States), Luciano Maiani Università di Roma La Sapienza (Italy), John Mather NASA Goddard Space Flight Center (United States), David Merritt Rochester Institute of Technology (United States), Viatcheslav Mukhanov LMU München (Germany), Giorgio Parisi Universita di Roma la Sapienza (Italy), Stuart Shapiro University of Illinois at Urbana-Champaign (United States), George Smoot Universite Paris Diderot (France), Saul Teukolsky Cornell University (United States), Kip Thorne California Institute of Technology (United States), Gabriele Veneziano Collège de (France) (France), Jean-Yves Vinet Virgo Collaboration Spokesperson, OCA Nice (France), Rainer Weiss MIT (United States), Clifford Will University of Florida (United States), Edward Witten Institute for Advanced Study, Princeton (United States), Arnold Wolfendale Durham University (United Kingdom), and Shing-Tung Yau Harvard University (United States). A complete list of supporters can be found at http://elisascience.org/supporters 2. The Gravitational Universe – Authors, Contributors, Supporters.

(3) +*#&%/")#+%* In the early years of this millennium, our view of the Universe has been comfortably consolidated in some aspects, but also profoundly changed in others. In 2003, the double pulsar PSR J0737-3039 was discovered [1–2], and General Relativity passed all of the most stringent precision tests in the weak-field limit. In 2013, the toughest test on General Relativity was performed through the observation of PSR J0348+0432, a tightly-orbiting pair of a newly discovered pulsar and its white-dwarf companion. Given the extreme conditions of this system, some scientists thought that Einstein’s equations might not accurately predict the amount of gravitational radiation emitted, but General Relativity passed with flying colours [3]. However, no test of General Relativity could be considered complete without probing the strong-field regime of gravitational physics, where mass motions are close to the speed of light, c, and gravitational potentials close to c2: Around a black hole, a central singularity protected by an event horizon, relativistic gravity is extreme. Exploring the physics of the inspiral of a small compact object skimming the event horizon of a large black hole, or the physics of a black hole-black hole collision, is probing gravity in the relativistic strong-field limit. 2013 marked an important date: ESA’s Planck mission confirmed the Λ-CDM paradigm of cosmology at an unprecedented level of accuracy, offering the most precise all-sky image of the distribution of dark matter across the entire history of the Universe [4], further confirming that the minuscule quantum fluctuations which formed at the epoch of inflation were able to grow hierarchically from the small to the large scale under the effect of the gravity of dark matter, and eventually evolved into the galaxies we observe today with their billions of stars and central black holes [5]. In the Λ-CDM model, the first black holes, called seeds, formed in dark matter halos from the dissipative collapse of baryons [6–7], and as halos clustered and merged, so did their embedded black holes [8–9]. As a consequence, binary black holes invariably form, driven by galaxy collisions and mergers, and trace the evolution of cosmic structures. In 2003 an ongoing merger between two hard X-ray galactic nuclei, with the characteristics of an Active Galactic Nucleus (AGN), was discovered just 150 Mpc away in the ultra-luminous infrared galaxy NGC 6240 (see Figure 1) [10]. Recent optical surveys have shown evidence of dual AGN [11] in today’s Universe; even Andromeda and our Milky Way are due to collide and both house a central black hole! Galaxy mergers were even more frequent in the past. The ensuing coalescence of massive black holes offers a new and unique tool, not only to test theories of gravity and the black hole hypothesis itself, but to explore the Universe from the onset of the cosmic dawn to the present. In 2000, we discovered that dormant black holes are ubiqThe Gravitational Universe – Introduction. uitous in nearby galaxies and that there are relationships between the black hole mass and the stellar mass of the host galaxy [12–13]. This gave rise to the concept that black holes and galaxies evolve jointly. Black holes trace galaxies and affect their evolution; likewise, galaxies trace black holes and affect their growth. Coalescing binary black holes pinpoint the places and times where galaxies merge, revealing physical details of their aggregation. This new millennium also witnessed the discovery of numerous ultra-compact binary systems containing white dwarfs and/or neutron stars in close orbit, in the Milky Way [14]. These are excellent laboratories for exploring the extremes of stellar evolution in binary systems. They will transform into Type Ia supernovae or into merging binaries which will soon be detected by the ground-based gravitational wave detectors LIGO and VIRGO. Stellar mass black holes with a pulsar as companion remain elusive, as they are very rare systems. Tracing these almost dark ultra-compact binaries of all flavours with gravitational waves all over the Milky Way will reveal how binary stars formed and evolved in the disc and halo of the Galaxy. Some of these are already known through electromagnetic observations and serve as guaranteed verification sources. All of these advances were possible using only our first ‘sense’ for observing the Universe, electromagnetic radiation, tracing electromagnetic interactions of baryonic matter in the Universe. However, almost all of the Universe remains electromagnetically dark. On astronomical scales gravitation is the real engine of the Universe. By ‘listening’ to gravity we will be able to see further than ever before. We can ‘listen’ to the Universe by directly observing gravitational waves, ripples in the fabric of spacetime travelling at the speed of light, which only weakly interact with matter and travel largely undisturbed over cosmological distances. Their signature is a fractional squeezing of spacetime perpendicuar to the direction of propagation, with an amplitude h = ∆L/L on the order of 10–20. Laser interferometry is a standard tool for such measurements and has been under development for over 30 years now [15]. Electromagnetic observations of the Universe, plus theoretical modelling, suggest that the richest part of the gravitational wave spectrum falls into the frequency range accessible to a space interferometer, from about 0.1 mHz to 100 mHz. In this band, important first-hand information can be gathered to tell us how binary stars formed in our Milky Way, and to test the history of the Universe out to redshifts of order z ~ 20, probing gravity in the dynamical strong-field regime and on the TeV energy scale of the early Universe [16]. eLISA will be the first ever mission to survey the entire Universe with gravitational waves, addressing the science theme The Gravitational Universe. The Next Gravitational Observatory (NGO) mission concept studied by ESA for the L1 mission selection is used as a strawman mission concept for eLISA [15]. ■ 3.

(4) In Sections I, II, and III, we will describe the eLISA observational capabilities in terms of an observatory sensitivity that is shown in Figure 12 as a U-shaped curve. The curve is based upon the sensitivity model of the strawman mission concept presented in Section IV. For the purpose of the discussion in Sections I, II, and III, this is just a baseline requirement. The question of how this requirement can be met, or exceeded, in an actual mission is addressed in Section IV.. +0(!'#&%-$1'+)!2(,2!)3($%2.' As we will discuss in more detail in this section, eLISA observations will probe massive black holes over a wide, almost unexplored, range of redshift and mass, covering essentially all important epochs of their evolutionary history. eLISA probes are coalescing massive binary black holes, which are among the loudest sources of gravitational waves in the Universe. They are expected to appear at the ‘cosmic dawn’, around a redshift of z ~ 11 or more, when the first galaxies started to form. Coalescing binary black holes at a redshift as remote as z ~ 20 can be detected with eLISA, if they exist. eLISA will also explore black holes through ‘cosmic high noon’ (a term introduced by [17]), at redshifts of z ~ 3 to z ~ 1.5, when the star formation rate in the Universe and the activity of Quasi Stellar Objects (QSOs) and AGNs was highest. In the ‘late cosmos’, at z < 1, eLISA will continue to trace binary mergers, but it will also detect new sources, the Extreme Mass Ratio Inspirals (EMRIs), i.e., the slow inspiral and merger of stellar mass black holes into large, massive black holes at the centres of galaxies. These are excellent probes for investigating galactic nuclei during the AGN decline.. +0+(4566789(:7;5<=(:>5?@(AB>96 The exploration of the sky across the electromagnetic spectrum has progressively revealed the Universe at the time of the cosmic dawn. The most distant star collapsing into a stellar mass black hole, the Gamma Ray Burst GRB 090429B, exploded when the Universe was 520 Myr old (at a redshift of z ~ 9.4), confirming that massive stars were born and died very early on in the life of the Universe [18]. The most distant known galaxy, MACS0647-JD, at a redshift of z ~ 10.7, was already in place when the Universe was about 420 Myr old [19], and ULAS J1120+0641 holds the record for being the most distant known QSO, thus the most distant supermassive (~ 109 M9) accreting black hole at redshift z ~ 7.08, about 770 Myr after the big bang [20]. Such observations clearly show that stars, black holes, and galaxies, the key, ubiquitous components of the Universe, were present before the end of the reionisation phase around z ~ 6 [21]. These are the brightest sources, probing only the peak of an underlying distribution of smaller objects: the less luminous pre-galactic discs, and the less massive stars and black holes, of which little is known. Even the brightest QSOs fade away in the optical regime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due to the presence of neutral hydrogen in the intergalactic medium (the Gunn-Peterson trough, [22]), and the search for the deepest sources using X-rays may be hindered by intrinsic obscuration, confusion due to crowding and the unresolved background light [23]. The entire zoo of objects, which in the past formed the small building blocks of the largest ones we see today, is so far pretty much unexplored. These primitive objects started to form at the onset of the cosmic dawn, around z ~ 20 – 30, according to current cosmological models [24]. In fact, simulations indicate that the very early pre-galactic, gas-rich discs had low masses, small luminosities and were very metal-poor. At an epoch of z ~ 20 to 30, the earliest stars may have had masses exceeding 100 M9, ending their lives as comparable stellar mass black holes, providing the seeds that would later grow into supermassive black holes [6, 25]. However, as larger, more massive and metal enriched galactic discs progressivly formed, other paths for black hole seed formation became viable (see [26] for a review). Global gravitational instabilities in gaseous discs may have led to the formation of quasi-stars of 103 – 104 M9 that later collapsed into seed black holes [7]. Further alternatives arise in the form of the collapse of massive stars formed in run-away stellar collisions in young, dense star clusters [27] or the collapse of unstable self-gravitating gas clouds in the nuclei of gas-rich galaxy mergers at later epochs [28]. Thus, the initial mass of seed black holes remains one of the largest uncertainties in the present theory of black hole formation, as the mechanism is still unknown, and the electromagnetic horizon too small for the direct detection of the formation of individual seeds. Most of the investigations of galaxies and AGNs in the electromagnetic Universe, in terms of richness of sources, focus on a later epoch: the cosmic high noon, a period around z ~ 1.5 – 3. This epoch features several critical The Gravitational Universe – Astrophysical Black Holes.

(5) Theoretical models developed in the context of the Λ-CDM paradigm [38–41] have been successful in reproducing properties of the observed evolution of galaxies and AGNs, such as the colour distribution of galaxies, the local mass density and mass function of supermassive black holes, and the QSO luminosity function at several wavelengths out to z ~ 6. Information about the underlying population of inactive, less massive and intrinsically fainter black holes, which grew through accretion and mergers across all cosmic epochs, is still lacking and difficult to gather. The Gravitational Universe proposes a unique, new way to probe both cosmic dawn and high noon, to address a number of unanswered questions: t When did the first black holes form in pre-galactic halos, and what is their initial mass and spin? t What is the mechanism of black hole formation in galactic nuclei, and how do black holes evolve over cosmic time due to accretion and mergers? t What is the role of black hole mergers in galaxy formation? eLISA will study the evolution of merging massive black holes across cosmic ages, measuring their mass, spin and redshift over a wide, as yet unexplored, range. Black holes with masses between 104 M9 and 107 M9 will be detected by eLISA, exploring for the first time the low-mass end of the massive black hole population, at cosmic times as early as z ~ 10, and beyond. 92+'!(F76?B89<=(FBQ57; Coalescing black hole binaries enter the eLISA sensitivity band from the low frequency end, sweeping to higher frequencies as the inspiral gets faster and faster, as shown in Figure 13. Eventually they merge, with the formation The Gravitational Universe – Astrophysical Black Holes. #". +,-./012,3040+,-./012,305367368. !). !"#$%&'#!%( )*#+,-#-,./#0&1#+% .'!%*+#-.*2. !' !& !"#$%&'()*+,. !# !". 34-4*% 56&"*.'%!. ) '. ". #. %. &. %" ". #. $" !" ". & !" #". transformations in galaxy evolution, since around that time both the luminous QSOs and the star formation rate were at their peak [29–30]. Galaxy mergers and accretion along filaments during cosmic high noon were likely to be the driving force behind the processes of star formation, black hole fueling, and galaxy growth. This turned starforming discs into larger discs or quenched spheroidal systems hosting supermassive black holes of billions of solar masses [31–33]. In this framework, massive black hole binaries inevitably form in large numbers, over a variety of mass scales, driven by frequent galaxy mergers [8–9, 34]. Signs of galaxy mergers with dual black holes at wide separations (on the order of kpc) come from observations of dual AGNs in optical and X-ray surveys, while observations of binary black holes with sub-pc scale separations remain uncertain and only candidates exist at present [35]. Studies of the dynamics of black holes in merging galaxies have shown that black hole coalescences trace the merger of the dense baryonic cores better than the mergers of dark halos, as their dynamics are sensitive to gas and star content and feed-back [36–37].. "" !". $ ' -./*010))), 9. (. ). *. !"#$%&'4)' 2>+9:,+:BA>+:>$%' -&;&-9' >=' :@&' 9D/' ,+7' 8>-,%"9,:">+' ,+#-&B ,;&%,#&7' F0G' =>%' &HIFJK' =>%' &L$,-' ?,99' +>+B98"++"+#' C"+,%"&9' ,9' ,' =$+A:">+'>=':@&"%':>:,-'%&9:'=%,?&'?,99K'!"',+7'A>9?>->#"A,-'%&79@"=:K'!E' #A9(C<5?@6(<9R<969;C(CA9(Q566H<9F6A7OC(98B>PC7B;(BO(69>9?C9F(6PR9<Q56H 6789(:>5?@(AB>96S(CDB(RB667:>9(98B>PC7B;5<=(R5CA6(OB<(5(:>5?@(AB>9(RBD9<H 7;I(5"]̰`š351 UVCTVKPIHTQOCOCUUKXGUGGFDNWGEWTXGQTHTQOC2QR +++UGGFHTQOCEQNNCRUGFOGVCNHTGGUVCT[GNNQYEWTXG CV[RKECNT̰09( DNCEMJQNGKPCIKCPVGNNKRVKECNICNCZ[ TGFEWTXG CPFC/KNM[9C[NKMGDNCEM JQNG ITGGPEWTXG %KTENGUOCTMDNCEMJQNGDNCEMJQNGOGTIGTUQEEWTTKPI 5>B;I(CA9(D5=0(#A969(D9<9(B:C57;9F(P67;I(6C5C9(BO(CA9(5<C(69Q7H5;5>=C7?5>( OGTIGT VTGG OQFGNUšUKVW0( #A9( I<9=( C<5;6R5<9;C( 5<95( 7;( CA9( :BCCBQ( <7IAC( EQTPGT TQWIJN[ KFGPVKƒGU VJG RCTCOGVGT URCEG HQT YJKEJ OCUUKXG DNCEM AB>96( Q7IAC( RBD9<( RA9;BQ9;5( CA5C( D7>>( >7@9>=( :9( B:69<85:>9( :=( OPCP<9( 9>9?C<BQ5I;9C7?(R<B:960(. of a common event horizon, followed by the ringdown phase during which residual deformation is radiated away and a rotating (Kerr) black hole remnant is formed. The waveform detected by eLISA is a measure of the amplitude of the strain in space as a function of time in the rest frame of the detector. This waveform carries information about the masses and spins of the two black holes prior to coalescence, the inclination of the binary plane relative to the line of sight, the luminosity distance and sky location, among other parameters [42]. Complete waveforms have been designed by combining Post Newtonian expansion waveforms for the early inspiral phase with an analytical description of the merger and ringdown phase, calibrated against highly accurate, fully general relativistic numerical simulations of black hole coalescence [43–44]. The first figure of merit of the eLISA performance is the signal-to-noise ratio (SNR) of a massive black hole binary coalescence with parameters in the relevant astrophysical range. Figure 2 shows eLISA SNRs for equal mass, nonspinning coalescing binaries. Here we compute the SNR as a function of the total mass, M, and of the redshift, z, averaging over all possible source sky locations and wave polarisations, assuming two-year observations. The plot highlights the extraordinary capabilities of the instrument in covering almost all of the mass-redshift parameter space needed to trace black hole evolution. Binaries with 104 M9 < M < 107 M9 can be detected out to z ~ 20 with an SNR ≥ 10, if they exist. Figure 2 shows that virtually all massive black holes in the Universe were loud eLISA sources at some point in their evolution. 5.

(6) Figure 3 shows error distributions in the source parameter estimation for events collected and extracted from a metacatalogue of ~ 1500 simulated sources. The catalogue is constructed by combining predicted merger distributions from a number of cosmological models encompassing a broad range of plausible massive black hole evolution scenarios [45]. Uncertainties are evaluated using the Fisher Information Matrix approximation, which gives an estimate of the errors on the inferred parameters. Figure 3 illustrates that individual redshifted masses can be measured with unprecedented precision, with an error of 0.1 % – 1 % (we recall that observations can only determine the redshifted source masses, i.e., the product of mass and (1 + z)). The spin of the primary black hole can be measured with very high accuracy, with 0.01 – 0.1 absolute uncertainty. Current theoretical models predict coalescence rates in the range 10 – 100 per year [46–48]. For more than 10 % of these, mostly occurring at a redshift of z < 5, the distance can be determined to better than a few percent and the sky location determined to better than a few degrees, which makes these sources suitable targets for coincident searches of electromagnetic counterparts (see Section V). !6C<BRA=67?5>(7QR5?C eLISA will allow us to survey the vast majority of all coalescing massive black hole binaries throughout the whole Universe. This will expose an unseen population of objects which will potentially carry precious information about the entire black hole population. It will provide both the widest and deepest survey of the sky ever, since gravitational wave detectors are essentially omni-directional by nature, and thus act as full-sky monitors. As highlighted in Figure 2, the range of black hole redshifts and masses that will be explored is complementary to the space explored by ./&0),+1-. '()*+,1. %&( %&'. %. %&). !#. !"#$%&'("#)*+$$),,2-. !$ % !"#$©%1&. $. '()*+,2. %. %&) %&(. %&'. %&'. %&# %. The present Universe is in a phase in which both the star formation rate and AGN activity are declining. In this late cosmos we observe quiescent massive black holes at the centres of galaxies within a volume of about 0.02 Gpc3 [51]. The current census comprises about 75 massive black holes out to z < 0.03. The black hole of 4 × 106 M9 at the Galactic Centre is the most spectacular example [52–53]. Thanks to its proximity, a young stellar population has been revealed precisely where no young stars were predicted to form, as star-forming clouds are expected to be tidally disrupted there [54]. This indicates our lack of understanding about the origin of stellar populations around black holes, and in particular stellar dynamics, even in our own Galaxy. By probing the dynamics of intrinsically dark, relic stars in the nearest environs of a massive black hole, eLISA will offer the deepest view of galactic nuclei, exploring phenomena inaccessible to electromagnetic observations [55–56]. The probes used are the so-called EMRIs: a compact star (either a neutron star or a stellar mass black hole) captured. ./&0),+2-. %&(. %&# !' !" !# !$ !% !$ !" !"#$©,2-,2&. !#. !$ % !"#$©%2&. $. %. !"#$%&'N)'&HIFJ'8,%,?&:&%'&9:"?,:">+',AA$%,A/'=>%'?,99";&'C-,AD'@>-&' C"+,%"&9'O'8%>C,C"-":/'7&+9":/'=$+A:">+9E'29OC(R5;9>6(6ABD(9<<B<6(B;(CA9( TGFUJKHVGF OCUU CPF TKIJV RCPGNU QP VJG URKPU 6QR RCPGNU TGHGT VQ VJG RTKOCT[DNCEMJQNGDQVVQORCPGNUVQVJGUGEQPFCT[DNCEMJQNG. 6. Black hole coalescence events will illuminate the physical process of black hole feeding. While the mass distribution carries information about the seeds, the spin distribution charts the properties of the accretion flows, whether they are chaotic or coherent [50]. Gravitational wave observations alone will be able to distinguish between the different evolution scenarios [46].. %&(. %&# !' !" !# !$ !% !$ !" !"#$©,1-,1&. eLISA will create the first catalogue of merging black holes, which will enable us to investigate the link between the growing seed population and the rich population of active supermassive black holes evolving during cosmic dawn and high noon. In doing this, we will probe the light end of the mass function at the largest redshifts and investigate the role of early black holes in cosmic re-ionisation and the heating of the intergalactic medium [49].. +++'ZVTGOG/CUU4CVKQ+PURKTCNU '/4+U. %&'. %&#. electromagnetic observations (see Figure 2).. %&) '()*+%1. !"#$%&'("#)*+$$),,1-. '()*+%2. %&). !"#$%&'5)'J+',%:"9:M9'"?8%&99">+'>=':@&'98,A&:"?&'>=',+'&.:%&?&B?,99B %,:">' "+98"%,-' ,+7' ,' %&8%&9&+:,:";&' <,;&=>%?' >=' :@&' &.8&A:&7' #%,;":,B :">+,-' <,;&9E( !( 6Q5>>9<( :>5?@( AB>9( B<:7C6( 5<BP;F( 5( 6PR9<Q566789( :>5?@( AB>90'!"#$%&'()*+*@. The Gravitational Universe – Astrophysical Black Holes.

(7) )*#. )*#. )*%. )*%. )*&. )*&. t What is the mass distribution of stellar remnants at the galactic centres and what is the role of mass segregation and relaxation in determining the nature of the stellar populations around the nuclear black holes in galaxies?. ). t Are massive black holes as light as ~105 M9 inhabiting the cores of low mass galaxies? Are they seed black hole relics? What are their properties?. )*#. )*#. )*%. )*%. )*&. )*&. eLISA will observe EMRI events, exploring the deepest regions of galactic nuclei, those near the horizons of black holes with masses close to the mass of the black hole at our Galactic Centre, out to redshifts as large as z ~ 0.7. Stellar mass black holes are expected to dominate the observed EMRI rate for eLISA, as mass segregation by two-body relaxation tends to concentrate the heaviest stars near the central, massive black hole [16, 57–58], and a stellar mass black hole inspiral has a higher SNR, so it can be detected out to farther distances. EMRIs can be tracked around a central black hole for up to 104 – 105 cycles on complex relativistic orbits (see Figure 5). As a consequence, the waveform carries an enormous amount #. ,-+.+//(")*"0*"-1('&%*,%&)+. +$.!"3*0%2".$3!"-4. $ % & " '& '% '$ '#. '!". '#. '$. '%. '&. ". &. %. $. #. !". 5-."6-4!*0%2".$3!"-4 !"#$%&'(")*#$+*'"*,-+.+//(")*"0*"-1('&%*,%&)+. )*+$,-.#%*#/0"!12$. %Ɩ!"'&&. &Ɩ!"'&&. !# !$ !% !' !& !" !# !$ !% !' !& !( !"#$©,.,&*+!"#$©-.-& !"#$©%1&. '()*+0 pl. 122"0(3&2&(4)+()/5607". ). ). 86+#36/95")*9*"0(. !" !# !$ !% !' !& !# !$ !% !' !& !( !"#$©1& !"#$©Epl .0pl+++&. ). ). +. !"#$%&'3)'&HIFJ'8,%,?&:&%'&9:"?,:">+',AA$%,A/'=>%'P*GI9E(#BR(>9OC(R5;H GNGUVKOCVKQPQHVJGTGFUJKHVGFOCUUGU ƒNNGFOCUUKXGDNCEMJQNGUQNKF NKPG UVGNNCT DNCEM JQNG VQR TKIJV RCPGN URKP QH VJG OCUUKXG DNCEM JQNG DQVVQO NGHV RCPGN GEEGPVTKEKV[ CV RNWPIG DQVVQO TKIJV RCPGN OKPKOWO Q956P<5:>9( F9875C7B;( BO( CA9( XP5F<PRB>9( QBQ9;C( BO( CA9( Q566789( :>5?@( AB>9(O<BQ(CA9(39<<(85>P90. of information [59]. Through observations of dark components alone, eLISA will detect EMRIs with an SNR > 20 in the mass interval for the central black hole between 104 M9 < M < 5 × 106 M9 out to redshift z ~ 0.7 (see Figure 13), covering a co-moving volume of 70 Gpc3, a much larger volume than observations of dormant galactic nuclei today. The estimated detection rates, based on the best available models of the black hole population and of the EMRI rate per individual galaxy [60], are about 50 events for a 2 year mission, with a factor of 2 uncertainty from the waveform modelling and lack of knowledge about the system parameters, and an additional uncertainty of at least an order of magnitude stemming from the uncertain dynamics of dense stellar nuclei [61–62]. As shown in Figure 6, the masses of both black holes are, in most cases, measured to better than one part in 104, the eccentricity at plunge is determined to a 10–4 accuracy, and the spin of the primary black hole to better than 10–3. The deviation of the quadrupole moment of the massive black hole with respect to the Kerr metric value is determined to better than 0.01, enabling unprecedented tests of General Relativity to be performed (see Section II). !6C<BRA=67?5>(7QR5?C. ". '&Ɩ!". '&&. '%Ɩ!"'&&. !". '()*+%1. ./&0),+1-. '()*+/. Key questions can be addressed in the study of galactic nuclei with EMRIs:. !"#$%&'("#)*+$$),,*+--. '()*+,*+-. in a highly relativistic orbit around the massive black hole and spiralling through the strongest field regions a few Schwarzschild radii from the event horizon before plunging into it (Figure 4).. ". &""". %""". $""". #""". !"""". !"#$%&'( !"#$%&'Q)'P*GI'>%C":',+7'9"#+,-E(+;(CA9(CBR(R5;9>(D9(699(CA9(I9BQ9C<7?5>( 6A5R9(BO(CA9(B<;5C9(<9>5C7876C7?(.4&+(B<:7C0(#A9(>BD9<(R5;9>(6ABD6(CA9(?B<H <96RB;F7;I(I<587C5C7B;5>(D589(5QR>7CPF9(56(5(OP;?C7B;(BO(C7Q90. The Gravitational Universe – Astrophysical Black Holes. In The Gravitational Universe, EMRIs are exquisite probes for testing stellar mass black hole populations in galactic nuclei. With eLISA we will learn about the mass spectrum of stellar mass black holes, which is largely unconstrained both theoretically and observationally. The measurement of even a few EMRIs will give astrophysicists a totally new way of probing dense stellar systems, allowing us to determine the mechanisms that govern stellar dynamics in the galactic nuclei [58]. 7.

(8) Measurements of a handful of events will suffice to constrain the low end of the massive black hole mass function, in an interval of masses where electromagnetic observations are poor, incomplete or even missing [63]. By 2028 the Large Synoptic Survey Telescope (LSST) will have observed a large number of tidal disruption events [64], which will also teach us a lot about black holes and stellar populations in galactic centres. However, these events will typically be on the higher end of the black hole’s mass function, and will not reveal masses with the same precision as eLISA, whose observations will give us information about the nature and the occupation fraction of massive black holes in low mass galaxies (as yet unconstrained)[65]. This will provide additional information about the origin of massive black holes, complementary to that gathered via observations of high z massive black hole mergers. EMRIs will also provide the most precise measurements of Milky Way type massive black hole spins, and make it possible for us to investigate the spin distribution of single, massive black holes up to z ~ 0.7. EMRIs can occur around black holes in all galaxies, regardless of their nature, i.e., whether they are active or not. As such, spin measurements will not be affected by observational uncertainties in the spectra of the AGN.. sufficient sensitivity to observe even small corrections to Einstein gravity. The strong-field realm of gravity theories can be probed near the event horizon of Kerr black holes or in other large-curvature environments (e.g., in the early Universe). Gravity can be thought of as strong in the sense that gravitational potentials are a significant fraction of c2 or in the sense that the curvature tensor (or tidal force) is of very large magnitude. Testing strong gravity takes on different meanings depending upon which notion of ‘strong gravity’ is being used. In any case, both are very important to test with high precision. The measurement of the anisotropy of the Cosmic Microwave Background (CMB) by ESA’s Planck satellite directly constrains properties of the quantum fluctuations during inflation which are thought to be the seeds of structure formation. This connection between physics on the smallest and largest scales is strong motivation for testing General Relativity to the highest possible accuracy, and in particular in the strong-field regime, where deviations could hint at a formulation of a quantum theory of gravity. The nature of gravity in the strong-field limit is, so far, largely unconstrained, leaving open several questions:. Detection rates will tell us about the density of stellar mass black holes in the vicinity of the central black hole, constraining the effectiveness of the mass segregation processes [66]. The measured eccentricity and orbital inclination distributions can be linked directly to the preferred channel of EMRI formation, giving us important clues about the efficiency of dynamical relaxation, and the frequency of binary formation and breakup in dense nuclei [67]. ■. t Does gravity travel at the speed of light ?. ++6*'.#951(0#674'. t Are astrophysical black holes fully described by the Kerr metric, as predicted by General Relativity?. This section covers tests of strong gravity and cosmology, two regimes where The Gravitational Universe will offer major advances.. t Does the graviton have mass? t How does gravitational information propagate: Are there more than two transverse modes of propagation? t Does gravity couple to other dynamical fields, such as, massless or massive scalars? t What is the structure of spacetime just outside astrophysical black holes? Do their spacetimes have horizons?. An outstanding way to answer these questions and learn about the fundamental nature of gravity is by observing the vibrations of the fabric of spacetime itself, for which coalescing binary black holes and EMRIs are ideal probes.. ++0+( $7IA( R<9?767B;( Q956P<9Q9;C6( BO( 6C<B;I( I<587C= .YR>B<7;I( <9>5C7876C7?( I<587C=( D7CA( :7;5<=( :>5?@( AB>9( Einstein’s General Relativity is one of the pillars of modern cosmology. The beauty of General Relativity is that it is a falsifiable theory: once the underlying mass distribution is identified to be a black hole binary system with fixed masses and spins, the theory has no further adjustable parameters. Thus even a single experiment incompatible with a prediction of the theory would lead to its invalidation, at least in the physical regime of applicability of the experiment. The Gravitational Universe will explore relativistic gravity in the strong-field, non-linear regime. It seems unlikely that any other methods will achieve the sensitivity of eLISA to deviations of strong-field gravity by 2028 (see Section V). Unlike the ground-based instruments, eLISA will have 8. OGTIGTUKPVJGUVTQPIƒGNFF[PCOKECNUGEVQT. The coalescence of a massive black hole binary with mass ratio above one tenth generates a gravitational wave signal strong enough to allow detection of tiny deviations from the predictions of General Relativity. The signal comprises three parts—inspiral, merger and ringdown—each of which probes strong-field gravity. The inspiral phase is well understood theoretically: It can last several months in-band, and it could be observed with an SNR of tens to hundreds by eLISA. The non-linear structure of General Relativity, and possible deviations from it, are encoded in the phase and amplitude of the gravitational waves. Any effect that leads to a cumulative dephasing of a significant fraction of a wave cycle over the inspiral phase can be deThe Gravitational Universe – The Laws of Nature.

(9) tected through matched filtering. Thousands of inspiral wave cycles will be observed, making it possible to detect even very small deviations in the inspiral rate predicted by General Relativity [68–71]. The propagation of gravitational waves can be probed through the dispersion of the inspiral signal. In General Relativity, gravitational waves travel with the speed of light (the graviton is massless) and interact very weakly with matter. Alternative theories with a massive graviton predict an additional frequency dependent phase shift of the observed waveform due to dispersion that depends on the graviton’s mass, mg, and the distance to the binary. An eLISA-like detector could set a bound around mg < 4 × 10–30 eV [72], improving current Solar System bounds on the graviton mass, mg < 4 × 10–22 eV, by several orders of magnitude. Statistical analysis of an ensemble of observations of black hole coalescences could also be used to place stringent constraints on theories with an evolving gravitational constant [73] and theories with Lorentz-violating modifications to General Relativity [74]. The inspiral is followed by a dynamical coalescence that produces a burst of gravitational waves. This is a brief event, comprising a few cycles and lasting about 5 × 103 sec (M/106 M9), yet it is very energetic, releasing 1059 (M/106 M9) ergs of energy, corresponding to 1022 times the power of the Sun. After the merger, the asymmetric remnant black hole settles down to a stationary and axisymmetric state through the emission of quasi-normal mode (QNM) radiation. In General Relativity, astrophysical black holes are expected to be described by the Kerr metric and characterised by only two parameters: mass and spin (the ‘no-hair’ theorem). Each QNM is an exponentially damped sinusoid with a characteristic frequency and damping time that depends only on these two parameters [75–77]. A measurement of two QNMs will therefore provide a strong-field verification that the final massive object is consistent with being a Kerr black hole [78–79]. The QNM spectrum of a black hole also has unique features which allow it to be distinguished from other (exotic) compact objects [80–83]. eLISA will observe ringdown signals with sufficient SNR to carry out these tests [84–86]. .YR>B<7;I(<9>5C7876C7?(I<587C=(D7CA(.4&+6(7;(CA9(6C<B;IH ƒGNFUVCVKQPCT[PQPNKPGCTTGIKOG EMRIs will provide a precise tool to probe the structure of spacetime surrounding massive black holes. The inspiralling compact object can generate hundreds of thousands of gravitational wave cycles while it is within ten Schwarzschild radii of the central black hole. These waveform cycles trace the orbit that the object follows, which in turn maps out details of the underlying spacetime structure, in a way similar to how stellar orbits have been used to precisely characterise the supermassive black hole at the centre of the Milky Way [87–88]. As seen in Figure 6, EMRI observations will not only proThe Gravitational Universe – The Laws of Nature. vide very precise measurements of the ‘standard’ parameters of the system, but will provide strong constraints on departures of the central massive object from the Kerr black hole of General Relativity [89]. The no-hair theorem tells us that the stationary axisymmetric spacetime around it should be completely determined by its mass and spin parameter. The gravitational wave signal from an EMRI occurring in a ‘bumpy’ black hole spacetime in which the multipole moments differ from their Kerr values would show distinctive, detectable signatures [89–94]. Figure 6 shows that 10 % deviations in the mass quadrupole moment, Q, from the Kerr value would be detectable for any EMRI observed with an SNR greater than 20. For typical systems, 0.1 % deviations will be detectable, and for the best systems, 0.01 % deviations will be detectable [59]. An observed inconsistency with the Kerr multipole structure might indicate a surprisingly strong environmental perturbation, the discovery of a new type of exotic compact object consistent with General Relativity, or a failure in General Relativity itself, but these possibilities will be observationally distinguishable (for a review of different hypotheses see [95–97]). These deviations could exhibit themselves in the following ways: For a boson star, the EMRI signal would not shut off after the last stable orbit [98]. For horizonless objects such as gravastars, the orbiting body would resonantly excite the modes of the (putative) membrane replacing the black hole horizon [99], and for certain non-Kerr axisymmetric geometries, orbits could become ergodic [100] or experience extended resonances [101]. Alternatives that will be testable with eLISA observations include the dynamical Chern-Simons theory [102–105], scalar-tensor theories (with observable effects in neutron star-black hole systems where the Neutron Star (NS) carries scalar charge [106]), Randall-Sundrum-inspired braneworld models [107–108] and theories with axions that give rise to ‘floating orbits’ [109]. Generic alternatives could also be constrained using phenomenologically parametrised models [110]. )B6QBI<5RA= The Gravitational Universe will use black hole binary mergers as ‘standard sirens’ to extract information on the expansion of the Universe, by measuring the expansion history with completely different techniques to electromagnetic probes. The term standard siren for gravitational wave sources, refers to a source that has its absolute luminosity encoded in its signal shape, analogous to a standard candle (like a Type Ia supernova) for electromagnetic sources. Black hole coalescences could serve as standard sirens for cosmography [111–112] by providing absolute and direct measurements of the luminosity distance, DL(z). When coupled with independent measurements of redshift, z, (for example, from associated transient electromagnetic sources ), these standard siren sources put points on the distance vs. redshift curve, and directly constrain 9.

(10) the evolution history of the Universe. Several mechanisms have been proposed that will provide an electromagnetic counterpart to massive black hole coalescences detectable by eLISA [113], however, confident identification might be viable only for low redshift events. Although rare, events at redshift z ≤ 1 – 2 are so loud that the baseline eLISA mission has the capability of localising them to within 10 square degrees, perhaps even 1 square degree, when information from the late merger of the black holes is included in the measurement model. This pins down these events on the sky well enough to allow searches for electromagnetic counterparts to the merger using wide area surveys such as LSST that will be active in 2028. With an associated counterpart, eLISA observations will allow 1 % measurements of DL(z) for 60 % of the sources, offering the prospect of ultra-precise determination of points on the distance-redshift curve that are completely independent of all existing constraints from Type Ia supernova, the CMB, etc. It is to be emphasised that there is no distance ladder in these measurements, since the luminosity distance is measured directly. This is possible because these sources are fundamentally understood, and General Relativity calibrates the distances. Weaker statistical constraints could also be derived in the absence of electromagnetic counterparts, using mergers at low redshift (z < 2) [114] or EMRIs [115–116]. EMRI observations could provide an independent measurement of H0 to a precision of a few percent. +QR5?C(B;(6?79;?9 The Gravitational Universe will permit unprecedented measurements of General Relativity in the strong-field regime. eLISA will map the spacetime around astrophysical black holes, yielding a battery of precision tests of General Relativity in an entirely new regime. These have the potential to uncover hints about the nature of quantum gravity, as well as enabling measurements of the properties of the Universe on the largest scales.. ++0++()B6QB>BI=(B;(CA9(#9Z(9;9<I=(6?5>9([(5( OB667>(:5?@I<BP;F(BO(I<587C5C7B;5>(D5896 Several processes occurring at very high energies in the primordial Universe can produce a stochastic background of gravitational waves. The detection of this relic radiation would have a profound impact both on cosmology and on high energy physics. Any fossil radiation of gravitational waves, if not washed away by inflation and later phase transitions, would have decoupled from matter and energy at the Planck scale. It can therefore directly probe cosmological epochs before the decoupling of the cosmic microwave background, currently our closest view of the big bang (Figure 7). The characteristic frequency of the gravitational waves is set by the horizon scale and therefore by the temperature of the Universe at the time of production. The eLISA frequency band of 0.1 mHz to 100 mHz corresponds to 0.1 to 100 TeV energy scales in the early Universe, at which new physics is expected to become visible. The 10. !"#$%&'R)'P;>-$:">+':"?&-"+&'SC"#'C,+#',+7':@&'&,%-/'T+";&%9&U',+7',':/8"B A,-'%,+7>?'<,;&=>%?'>=':@&'&.8&A:&7'#%,;":,:">+,-'<,;&9E(J<587C5C7B;5>( D5896(5<9(CA9(B;>=(D5=(CB(699(:9=B;F(CA9(?B6Q7?(Q7?<BD589(:5?@I<BP;F0( %TGFKV0#5#9/#2UEKGPEGVGCO. Large Hadron Collider (LHC) has been built to investigate the physics operating at this energy scale, and in 2012 the experiment produced with the remarkable discovery of the Higgs boson which has completed the particle spectrum of the Standard Model. It is the final confirmation that spontaneous symmetry breaking is the mechanism at play in electroweak physics, and is the first example of a fundamental scalar field playing a role in a phase transition that took place in the very early Universe. These findings further motivate the search for a cosmic background of gravitational waves. eLISA would have the sensitivity to detect a relic background created by new physics active at TeV energies if more than a modest fraction, ΩGW ~ 10–5 of the energy density of the Universe is, converted to gravitational radiation at the time of production. A gravitational wave detector in space has the potential to revolutionise our understanding of the physics of the infant Universe by exploring the microphysical behaviour of matter and energy through the direct detection of gravitational waves produced at this epoch, rather than by observing collisions of elementary particles. /76?B89<=(6R5?9 Abundant evidence suggests that the physical vacuum has not always been in its current state, and in many theories beyond the Standard Model, the conversion between vacuum states corresponds to a first-order phase transition. As the Universe expands and its temperature drops below the critical temperature, bubbles of a new phase form, expand, and collide, generating relativistic bulk flows, whose energy then dissipates in a turbulent cascade. The corresponding acceleration of matter radiates gravitational waves on a scale not far below the horizon scale [117–120]. eLISA could detect these gravitational waves, thus probing the Higgs field self couplings and potential, and the possible presence of supersymmetry, or of conformal dynamics at TeV scales. In general, since the Hubble length at the TeV scale is about 1 mm, the current threshold at which The Gravitational Universe – The Laws of Nature.

(11) the effects of extra dimensions might appear happens to be about the same for experimental gravity in the laboratory and for the cosmological regime accessible to eLISA, thus allowing eLISA to probe the dynamics of warped sub-millimetre extra dimensions, present in the context of some string theory scenarios [121–122]. In some braneworld scenarios the Planck scale itself is not far above the TeV scale. Consequently, the reheating temperature would be in the TeV range and eLISA could probe inflationary reheating. After inflation the internal potential energy of the inflaton is converted into a thermal mix of relativistic particles, which can generate gravitational waves with an energy of about 10–3 or more of the total energy density[123–125]. eLISA could also probe gravitational waves produced directly by the amplification of quantum vacuum fluctuations during inflation, in the context of some unconventional inflationary models, such as pre-big bang or bouncing brane scenarios[126–128]. Phase transitions often lead to the formation of one-dimensional topological defects known as cosmic strings. Fundamental strings also arise as objects in string theory and, although formed on submicroscopic scales, it has been realised that these strings could be stretched to astronomical size by cosmic expansion [129–130]. Cosmic strings interact and form loops which decay into gravitationl waves; eLISA will be the most sensitive probe for these objects, offering the possibility of detecting direct evidence of fundamental strings. The spectrum from cosmic strings is distinguishably different from that of phase transitions or any other predicted source [130]: It has nearly constant energy per logarithmic frequency interval over many decades at high frequencies, offering the possibility of simultaneous detection by eLISA and ground-based interferometers. Moreover, if strings are not too light, occasional distinctive gravitational wave bursts might be observed from kinks or cusps on string loops. If detected, these individual bursts will provide irrefutable evidence for a cosmic string source. ■. +++0("2#&!H)%4-!)#(,+*!&+.'(+*( 6*'/+.-;9#; Only a minority of the stars in the Universe are companionless, the majority being part of binary or multiple star systems (Figure 8). About half of the binaries form with sufficiently small orbital separations to interact and evolve into compact systems, often with white dwarfs, neutron stars, or possibly stellar mass black holes as components. The shortest period systems, known as ultra-compact binaries, are important sources of gravitational waves in the mHz frequency range [131]. These binaries are the outcome of one or more common-envelope phases that occur when one star evolves to the giant or supergiant stage. Unstable mass exchange leads to a short-lived phase in which. !"#$%&'V)'I--$9:%,:">+'>=','A>?8,A:'C"+,%/'9:,%'9/9:&?',+7','%&8%&9&+:,B :";&'<,;&=>%?'>=':@&'&.8&A:&7'#%,;":,:">+,-'<,;&9E(#DB(6C5<6(B<:7C7;I( 95?A( BCA9<( 7;( 5( F95CA( I<7R( 5<9( F96C7;9F( CB( Q9<I9( 5>>( CA9( DA7>9( O>BBF7;I( 6R5?9(D7CA(I<587C5C7B;5>(D58960(!"#$%&'(I+J!9K@G#""C@. the stellar core and the companion spiral towards each other, transferring angular momentum to the extended envelope of the giant that is blown away, leaving a tight binary system behind. This a necessary step in the formation of X-ray binaries, binary pulsars and double white dwarf binaries, observed in a variety of states and configurations [132]. Altough the Milky Way is full of these sources, only a tiny fraction are currently observed and studied indepth through observations from radio to X-rays. After the common-envelope phase, the compact stars in the binary are well separated, but evolve with shorter and shorter orbital periods due to the angular momentum loss via gravitational waves, until eventually the stars undergo another mass exchange once they reach orbital periods of minutes or less. Depending on the nature of the compact objects, they either merge or survive. Double neutron star binaries ultimately merge in bursts of high-frequency gravitational waves, potentially emitting a burst of electromagnetic radiation in the form of a short Gamma-Ray Burst. Although predicted to exist, no neutron star-stellar mass black hole binary or black hole-black hole binary has yet been detected. For binaries with a white dwarf component, mass loss is delicately balanced against loss of angular momentum, the outcome of which is unclear. Almost always, the loss of energy through gravitational waves is so strong that it causes the system to merge and possibly to end in a Type Ia or sub-luminous supernova explosion [133–134] or in (rapidly spinning) neutron stars that may have millisecond radio pulsar or magnetar properties [135]. In the remaining small fraction of cases, the mass transfer stabilises the system and long-lived interacting binaries are formed (as in the AM CVn systems if the companion is a white dwarf, or ultra-compact X-ray binaries if it is a neutron star). The physics of this evolutionary junction is rich and diverse, it involves tides, mass transfer, highly super-Eddington accretion, and mass ejection. eLISA will provide the data necessary for us to quantify the roles that these various physical processes play.. The Gravitational Universe – Ultra-compact binaries in the Milky Way. 11.

(12) Currently fewer than 50 ultra-compact binaries are known, only two of which have periods less than 10 minutes [14]; eLISA will discover several thousand of these. These systems are relatively short-lived and electromagnetically faint, but several known verification binaries are strong enough gravitational wave sources that they will be detected within weeks by eLISA. The discovery of many new ultra-compact binaries is one of the main objectives of eLISA, as it will provide a quantitative and homogeneous study of their populations and the astrophysics governing their formation. It also adds an additional facet to the knowledge of the Milky Way’s structure: The distribution of sources in the thin disc, thick disc, halo and its globular clusters (known breeding grounds for the formation of compact binaries via dynamical exchanges) [136]. These detections will enable us to address a number of key questions: t How many ultra-compact binaries exist in the Milky Way? t What is the merger rate of white dwarfs, neutron stars and stellar mass black holes in the Milky Way (thus better constraining the rate of the explosive events associated with these sources)? t What does that imply for, or how does that compare to, their merger rates in the Universe? t What happens at the moment a white dwarf starts mass exchange with another white dwarf or neutron star, and what does it tell us about the explosion mechanism of type Ia supernovae? t What is the spatial distribution of ultra-compact binaries, and what can we learn about the structure of the Milky Way as a whole? To answer these questions eLISA will observe thousands of individual sources and for the first time capture the signal from a foreground of sources, the sound of millions of tight binaries.. /76?B89<=(6R5?9 The vast majority of ultra-compact binaries will form an unresolved foreground signal in eLISA [137] as shown in Figure 13. Its average level is comparable to the instrument noise, but due to its strong modulation during the year (by more than a factor of two) it can be detected. The overall strength can be used to learn about the distribution of the sources in the Galaxy, as the different Galactic components (thin disc, thick disc, halo) contribute differently to the modulation [138]. Their relative amplitudes can be used to set upper limits on the, as yet completely unknown, halo population [139]. For a two-year eLISA mission, several thousand binaries are expected to be detected individually with an SNR > 7 [140] and their periods (below one hour and typically 5 – 10 min) determined from the periodicity of the gravitational wave signal. For many systems it will be possible to measure the 12. first time derivative of the frequency, and thus determine the chirp mass (a combination of the masses of the two stars that can be used to distinguish white dwarf, neutron star and black hole binaries) and the distance to the source. For more than 100 sources concentrated around the inner Galaxy, we expect distance estimates with accuracies better than 1 %, enabling us to make a direct measurement of the distance to the Galactic Centre. The number of ultra-compact binaries with neutron star or black hole components is still highly uncertain [141]. With eLISA operating as an all sky monitor, these systems can be observed throughout the Milky Way, providing a complete sample of binaries at the shortest periods (below 30 minutes), including ones containing stellar mass black holes, if they exist. The number of sources detected at mHz frequencies is directly related, via the gravitational wave orbital decay time scale, both to the number of systems formed at larger separations, and to the number of mergers. Therefore, the thousands of eLISA detections will also probe the formation of these binaries and their coalescence rates. Using eLISA, the sky position of about fifteen hundred sources will be determined to better than ten square degrees and more than half will have their distance determined to better than 20 % [142]. Several hundred of these may be found with current and future wide-field instruments such as the Visible and Infrared Survey Telescope for Astronomy (VIRCAM) and LSST. A few dozen of the highest SNR sources will have error boxes that are significantly smaller and can be realistically found with small field of view (several arcmin) cameras such as the Multiadaptive Optics Imaging Camera for Deep Observations (MICADO) on the European Extremely Large Telescope (E-ELT) or the James Webb Space Telescope (JWST).. !6C<BRA=67?5>(7QR5?C The large number of ultra-compact binaries discovered, and the fact that the sample is complete at the shortest periods, will help determine the total number of systems of all types as well as their merger rates. The systems containing neutron stars and/or black holes will be observed about a million years prior to coalescence, a phase that is still unexplored. The highest SNR systems will allow a study of the complex physics of white dwarf mergers or of how systems survive as interacting binaries. Recent detailed simulations [143] have cast doubt on the theory that the actual merger would be a truly dynamical process taking only one or two orbits, and instead show that the merger would take place over many orbits, possibly allowing eLISA to observe some mergers directly. eLISA will detect ultra-compact binaries beyond the Galactic Centre and in the Milky Way’s halo using observations which are unaffected by dust obscuration, providing an independent probe of the components and formation history of the Milky Way. ■. The Gravitational Universe – Ultra-compact binaries in the Milky Way.

(13) +8#564#9/#0/+55+10(14 #$.(92+'!('-!).(J&!Z+#!#+%*!2( 9#8'1$5'48#614; All of the above scientific objectives can be addressed by a single L-class mission consisting of 3 drag-free spacecraft forming a triangular constellation with arm lengths of one million km and laser interferometry between “free-falling” test masses. The interferometers measure the variations in light travel time along the arms due to the tidal deformation of spacetime by gravitational waves. Compared to the Earth-based gravitational wave observatories like LIGO and VIRGO, eLISA addresses the much richer frequency range between 0.1 mHz and 1 Hz, which is inaccessible on Earth due to arm length limitations and terrestrial gravity gradient noise. The Next Gravitational wave Observatory (NGO) mission studied for the L1 selection [15] is an eLISA strawman mission concept. It enables the ambitious science program described here, and has been evaluated by ESA as both technically feasible and compatible with the L2 cost target. Its foundation is mature and solid, based on decades of development for LISA, including a mission formulation study, and the extensive heritage of flight hardware and ground preparation for the upcoming LISA Pathfinder geodesic explorer mission, which will directly test most of the eLISA performance and validate the eLISA instrumental noise model [144–145].. 47667B;(F967I; The NGO mission has three spacecraft, one ‘mother’ at the vertex and two ‘daughters’ at the ends, which form a single Michelson interferometer configuration (Figure 9). The spacecraft follow independent heliocentric orbits without any station-keeping and form a nearly equilateral triangle in a plane that is inclined by 60° to the ecliptic. The constellation follows the Earth at a distance between 10° and !"#$%&'( )*+. !"#$%. !'"/"0'1. !"#$"%!&'"()**)+,"-(.. !"#. !"#$. !"#$%&'(6)'&HIFJ'W%C":9E(#A9(CA<99(92+'!H*J%(6R5?9?<5OC(OB>>BD(CA9(.5<CA( CUCPCNOQUVUVKHHVTKCPINGRWTGN[FWGVQEGNGUVKCNOGEJCPKEU. 30°, as shown in Figure 10. Celestial mechanics causes the triangle to rotate almost rigidly about its centre as it orbits around the sun, with variations of arm length and opening angle at the percent level. The payload consists of four identical units, two on the mother spacecraft and one on each daughter spacecraft (Figure 11). Each unit contains a Gravitational Reference Sensor (GRS) with an embedded free-falling test mass that acts both as the end point of the optical length measurement, and as a geodesic reference test particle. A telescope with 20 cm diameter transmits light from a 2 W laser at 1064 nm along the arm and also receives a small fraction of the light sent from the far spacecraft. Laser interferometry is performed on an optical bench placed between the telescope and the GRS. On the optical bench, the received light from the distant spacecraft is interfered with the local laser source to pro-. !"#$%&'( )*+. )*+. 2'1. &'(. 4+2&/5,. 0()'+ )2*+1' /,*,0(1%,. !"#$%%$&'"(#. ( !"()**)+,"-. $%&'()* +,-(.. 6.)0,47,&,3 &'()*+'&',-) (,./0()'+/12,-+20 !"#$%. 83)9:;3,, (1-&31* !"# !". !"#$%%$&'"(# $%#$% 2)0,340153(,. ,-&%'(.)*+ )LJXUHH/,6$FRQ̧JXUDWLRQ QRWWRVFDOH

(14) (%;9(QBCA9<(5;F(CDB(F5PIAH C9<(6R5?9?<5OC(9Y?A5;I7;I(>569<(>7IAC(OB<Q(5(CDBH5<Q(47?A9>6B;(7;C9<O9<H QOGVGT6JGTGCTGHQWTKFGPVKECNRC[NQCFUQPGCVVJGGPFQHGCEJCTOCU UJQYPKP(KIWTG. /.350&,30. 3'4'+',1' "2.*0(-2+. !"#$%&'(()'&HIFJ'8,/->,7E'CEJRC[NQCFWPKVEQPVCKPUCšEOVGNGUEQRG VJGVGUVOCUUGPENQUGFKPUKFGVJG)TCXKVCVKQPCN4GHGTGPEG5GPUQT )45 CPFCPQRVKECNDGPEJJQUVKPIVJGKPVGTHGTQOGVGTU #WZKNKCT[TGHGTGPEGKPH VGTHGTQOGVGTQOKVVGFHQTENCTKV[UGGš=?HQTFGVCKNU. The Gravitational Universe – The eLISA Space Gravitational Wave Observatory. 13.

(15) /<5IHO<99(?B;C<B> The spacecraft are actively controlled to remain centred on the test masses along the interferometric axes, without applying forces on the test masses along these axes. This ‘drag-free control’ around the shielded geodesic reference test masses uses the local interferometry measurement as a control signal for an array of micro-Newton spacecraft thrusters, with the residual spacecraft jitter reaching the nm/√ Hz level. These thrusters also control the spacecraft angular alignment to the distant spacecraft by detecting the laser beam wavefront with ‘differential wavefront sensing’ with nrad/√ Hz precision. Other degrees of freedom are controlled with electrostatic test mass suspensions. The only remaining degree of freedom is then the opening angle between the arms at the master spacecraft, which varies smoothly by roughly 1.5° over the year, and can be compensated for either by moving the two optical assemblies against each other or by a steering mirror on the optical bench. The test masses are 46 mm cubes, made from a dense nonmagnetic Au-Pt alloy and shielded by the GRS. The GRS core is a housing of electrodes, at several mm separation from the test mass, used for nm/√ Hz precision capacitive sensing and nN-level electrostatic force actuation on all non-interferometric degrees of freedom. The GRS also includes fibres for UV light injection for photoelectric discharge of the test mass, and a caging mechanism for protecting the test mass during launch and then releasing it in orbit. The GRS technology is direct heritage from LISA Pathfinder.. '9;67C787C= The strain sensitivity (shown in Figure 12) corresponds to the noise spectrum of the instrument. At low frequencies, it is dominated by residual acceleration noise of 3 fm s–2/√ Hz per test mass. Above about 5 mHz, arm length measurement noise dominates, for which 12 pm/√ Hz are allocated, out of which 7.4 pm/√ Hz are 14. ). ./"01&)21&#0")34#'/"02)5#&31/()*67))+8 -. !"#!% 9''#2#"0/1:&)&:13#)*6)/#3/);033+Ɩ!"#!%,-,.#!/,,,01. !"#!) !"#!(. 9";2#&@/?)"#34:&3# !"&,-,2"3!%,01,456#7889. !"#!' !"#!&. <&/#"=#":;#/"( *1&'2>)3?:/)&:13#!$Ɩ!"#!$,-/,,,01. !"#$" !"#%. !"#*. !"#+. !"#$. !"#!. !. !"#$%#&'()*+,!"#$%&'(4)' X"?&K' 9D/' ,+7' 8>-,%"9,:">+' ,;&%,#&7' &HIFJ' 9&+9":";":/E( #A9( PQKUGURGEVTWO UVTCKPUGPUKVKXKV[ KURNQVVGFCUCNKPGCTURGEVTCNFGPUKV[ !"#!( !"#$#%&'$()&(%*)&$#(+*#,-.(&/0'. duce a heterodyne beat note signal between 5 and 25 MHz, which is detected by a quadrant photodiode. The phase of that beat note is measured with µcycle/√ Hz precision by an electronic phasemeter. Its time evolution reflects the laser light Doppler shift from the relative motion of the spacecraft, and contains both the macroscopic arm length variations on times cales of months to years, and the small fluctuations with periods between seconds and hours that represent the gravitational wave science signal. The measurement of relative spacecraft motion is then summed with a similar local interferometer measurement of the displacement between test mass and spacecraft. This yields the desired science measurement between distant free-falling test masses, removing the much larger motion of the spacecraft, which contains both thruster and solar radiation pressure noise.. 8+)-($#.) 9#.#%&(%*:(+#$(') $*DKPCT[ ,-./01-2 3456 XGTKƒ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ƉŢHTGSWGPE[ŢQTVKOGUƉQH ;PQ:9<(?=?>96(6R9;C(:=(CA9(6BP<?9(5C(5(I789;(O<9XP9;?=(FP<7;I(CA9(B:69<H 85C7B;(OB<(QB;B?A<BQ5C7?(6BP<?960(#A9(C<5?@6(BO(CDB(Q566789(:>5?@(AB>9( DKPCTKGUNQECVGFCVLššYKVJGSWCNOCUUGU ]CPFK̰09 CTGUJQYP 6JG UQWTEG HTGSWGPE[ CPF 504 KPETGCUGU YKVJ VKOG CPF VJG TGOCKPH 7;I(C7Q9(:9OB<9(CA9(R>P;I9(76(7;F7?5C9F(B;(CA9(C<5?@60(!;(9XP785>9;C(R>BC( KU UJQYP HQT CP '/4+ UQWTEG CV š/RE YKVJ JCTOQPKE HTGSWGPEKGU GXQNXKPI UKOWNVCPGQWUN[ 5GXGTCN VJQWUCPF ICNCEVKE DKPCTKGU YKVJ 504U CDQXGYKNNDGTGUQNXGFCHVGT[GCTQHQDUGTXCVKQP5QOGDKPCT[U[UVGOU CTGCNTGCF[MPQYPCPFYKNNUGTXGCUXGTKƒECVKQPUKIPCNU/KNNKQPUQHQVJGT :7;5<796(<96P>C(7;(5(\?B;OP67B;(;B769E(CA5C(85<796(B89<(CA9(=95<0(#A9(589<5I9( >989>(76(<9R<969;C9F(56(I<9=(6A5F9F(5<950. quantum mechanical photon shot noise. At the highest frequencies, the sensitivity decreases again since multiple wavelengths of the gravitational wave fit into the arms, causing partial cancellation of the signal. A unique feature of the eLISA interferometry is the virtual elimination of the effects of laser frequency noise. Stabilisation to a reference cavity built into the payload is not enough to suppress it completely. The remaining noise is removed by ‘Time-Delay Interferometry’ (TDI) [146], which synthesises a virtual balanced arm length interferometer in postprocessing. This requires knowledge of the absolute arm lengths to roughly 1 m accuracy, measured via an auxiliary ranging phase modulation imposed on. The Gravitational Universe – The eLISA Space Gravitational Wave Observatory.